To find the odd one out in the series: 150, 160, 191, 214, 240, 240, 270, 305, we will analyze the differences between the consecutive numbers and identify any inconsistencies.
### Step-by-Step Solution:
1. **Identify the Series**:
The given series is: 150, 160, 191, 214, 240, 240, 270, 305.
2. **Calculate the Differences**:
- Difference between 150 and 160:
\( 160 - 150 = 10 \)
- Difference between 160 and 191:
\( 191 - 160 = 31 \)
- Difference between 191 and 214:
\( 214 - 191 = 23 \)
- Difference between 214 and 240:
\( 240 - 214 = 26 \)
- Difference between 240 and 240:
\( 240 - 240 = 0 \)
- Difference between 240 and 270:
\( 270 - 240 = 30 \)
- Difference between 270 and 305:
\( 305 - 270 = 35 \)
3. **List the Differences**:
The differences we calculated are:
10, 31, 23, 26, 0, 30, 35.
4. **Analyze the Pattern**:
We notice that the differences do not follow a consistent pattern. Let's analyze further:
- The first difference is 10.
- The second difference is 31, which is significantly larger than the first.
- The third difference is 23, which is less than 31.
- The fourth difference is 26, which is also inconsistent.
- The fifth difference is 0, which is unusual.
- The sixth difference is 30, and the seventh is 35.
5. **Identify the Anomaly**:
The difference of 0 (between the two 240s) is particularly suspicious. This suggests that one of the numbers might be incorrect.
6. **Re-evaluate the Series**:
To maintain a consistent pattern, we can hypothesize that the second number (160) might be incorrect. If we adjust it, we can try to find a number that fits better.
7. **Find a Suitable Replacement for 160**:
If we assume the difference after 150 should be 20 instead of 10, we can calculate:
- New number = 150 + 20 = 170.
8. **Reconstruct the Series**:
If we replace 160 with 170, the series becomes:
150, 170, 191, 214, 240, 240, 270, 305.
Now, let's recalculate the differences:
- Difference between 150 and 170:
\( 170 - 150 = 20 \)
- Difference between 170 and 191:
\( 191 - 170 = 21 \)
- Difference between 191 and 214:
\( 214 - 191 = 23 \)
- Difference between 214 and 240:
\( 240 - 214 = 26 \)
- Difference between 240 and 240:
\( 240 - 240 = 0 \)
- Difference between 240 and 270:
\( 270 - 240 = 30 \)
- Difference between 270 and 305:
\( 305 - 270 = 35 \)
9. **Conclusion**:
The new differences show a more consistent pattern, confirming that 160 is indeed the odd one out. The correct number should be 170.
### Final Answer:
The odd one out in the series is **160**.
